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Animal Crossing

There are three dogs and three cats that have to be transported across a river: a big dog, a medium dog and a small dog, a big cat, a medium cat, and a small cat. The boat can carry two animals, and all of the animals can row.

The medium dog cannot be left alone with either of the other dogs, nor can the medium dog be transported with another dog, because if the two are by themselves they will fight. The big dog will not fight with the small dog. Also the medium cat cannot be left alone with either of the other cats, nor can the medium cat be transported with another cat for the same reason, and the big cat never fights with the small cat.

To make matters worse, if ever there are more dogs than cats together on the shore, the dogs will fight with the cats.

How can the animals get across the river without a fight breaking out?

This is from 536 puzzles and curious problems by H. E. Dudeney, where it is called Crossing the ferry. Dudeney's problem featured squabbling families rather than cats and dogs. The solution provided in the book is incorrect. 

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